AZAÏS, Romain; GENADOT, Alexandre

doi:10.1002/9781119507338.ch3

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AZAÏS, Romain
Reproduction et développement des plantes [RDP]
Simulation et Analyse de la morphogenèse in siliCo [MOSAIC]

GENADOT, Alexandre
Quality control and dynamic reliability [CQFD]
Institut de Mathématiques de Bordeaux [IMB]

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Statistical Inference for Piecewise-deterministic Markov Processes, Statistical Inference for Piecewise-deterministic Markov Processes. 2018-08-06p. 65-105

Wiley

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This chapter discusses a particular piecewise‐deterministic Markov process (PDMP) to catastrophic events occurring at random times and with random intensities. It considers the insurance model by Kovacevic and Pflug describing the evolution of a capital subject to random heavy loss events. The chapter presents a local‐time crossing relation for the PDMP. This local‐time crossing relation allows for the proof of the so‐called Kac‐Rice formula, giving an explicit form for the average number of continuous crossings by the process of a given level. The chapter provides the results on the estimation of the absorption probability and hitting time for the PDMP. The motion of the process depends on an easily estimable quantity in a parametric, semi‐parametric or non‐parametric setting. The chapter focuses on a procedure for estimating the Markov kernel R of the post‐jump locations, formula leads to estimate the transition density by the plug‐in estimator.< Réduire

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Level Crossings and Absorption of an Insurance Model

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